Simplify the following expression: $ n = \dfrac{-8k - 4}{k + 6} - \dfrac{-4}{5} $
In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{-8k - 4}{k + 6} \times \dfrac{5}{5} = \dfrac{-40k - 20}{5k + 30} $ Multiply the second expression by $\dfrac{k + 6}{k + 6}$ $ \dfrac{-4}{5} \times \dfrac{k + 6}{k + 6} = \dfrac{-4k - 24}{5k + 30} $ Therefore $ n = \dfrac{-40k - 20}{5k + 30} - \dfrac{-4k - 24}{5k + 30} $ Now the expressions have the same denominator we can simply subtract the numerators: $n = \dfrac{-40k - 20 - (-4k - 24) }{5k + 30} $ Distribute the negative sign: $n = \dfrac{-40k - 20 + 4k + 24}{5k + 30}$ $n = \dfrac{-36k + 4}{5k + 30}$